Everyone does have the right to become an American citizen, as long as they fulfill some requirements. Obviously, there is a citizenship test. People cannot be allowed to vote in a country where they cannot understand what they are voting for. Also, people need to physically come here. If they can't get to America, the government has no duty to bring potential immigrants into the country.
There are many arguments against immigration. Numbers side with immigrants more than they do those that want to close our borders. Every person that lives here puts money into our system. At the very least money goes into food and housing. Few people want to come to this country for a free ride. They want to come here for a better life and they are usually happy to work hard for it.